Isoclinism and factor set in regular Hom-Lie Superalgebras

TL;DR

This paper introduces the concepts of isoclinism and factor set in regular Hom-Lie superalgebras, showing that finite-dimensional regular Hom-Lie superalgebras are isoclinic if and only if they are isomorphic.

Contribution

It extends the theory of Hom-Lie superalgebras by defining isoclinism and factor sets, and establishes a key isomorphism criterion for finite-dimensional cases.

Findings

Two finite-dimensional regular Hom-Lie superalgebras are isoclinic iff they are isomorphic.

Introduces isoclinism and factor set concepts in the context of Hom-Lie superalgebras.

Provides a characterization of isoclinic regular Hom-Lie superalgebras.

Abstract

Hom-Lie superalgebras can be considered as the deformation of Lie superalgebras; which are $\mathbb{Z}_2$-graded generalization of Hom-Lie algebras. The motivation of this paper is to introduce the concept of isoclinism and factor set in regular Hom-Lie superalgebras. Finally, we obtain that two finite same dimensional regular Hom-Lie superalgebras are isoclinic if and only if they are isomorphic.